Games and Meta-Games: Pricing Rules for Combinatorial Mechanisms

TL;DR

This paper introduces a new framework for designing near-incentive-compatible pricing mechanisms in combinatorial auctions by modeling the problem as a meta-game and analyzing its equilibrium.

Contribution

It provides a novel characterization of approximate incentive-compatibility through a meta-game approach, leading to a variational problem and solutions for optimal pricing.

Findings

Closed-form solutions in restricted cases

Numerical methods for general cases

Theoretical foundation for approximate incentive-compatibility

Abstract

In settings where full incentive-compatibility is not available, such as core-constraint combinatorial auctions and budget-balanced combinatorial exchanges, we may wish to design mechanisms that are as incentive-compatible as possible. This paper offers a new characterization of approximate incentive-compatibility by casting the pricing problem as a meta-game between the center and the participating agents. Through a suitable set of simplifications, we describe the equilibrium of this game as a variational problem. We use this to characterize the space of optimal prices, enabling closed-form solutions in restricted cases, and numerically-determined prices in the general case. We offer theory motivating this approach, and numerical experiments showing its application.